A circus tent is in the shape of a square pyramid. Each edge of the square base is 20 m and its slant height is 13.5 m. Find the height of the tent. Round the answer to the nearest tenth.(1 point)
Responses
A
14.8 cm
B
24.1 cm
C
16.8 m
D
9.1 m
To find the height of the tent, we can use the Pythagorean Theorem.
Let's label the height of the pyramid as 'h'.
The slant height of the pyramid forms a right triangle with half of the base of the pyramid as one leg, and the height of the pyramid as the other leg.
Using the Pythagorean Theorem, we have:
(1/2 * 20)^2 + h^2 = 13.5^2
10^2 + h^2 = 13.5^2
100 + h^2 = 182.25
h^2 = 182.25 - 100
h^2 = 82.25
Taking the square root of both sides, we get:
h ≈ 9.1 m
Therefore, the height of the tent is approximately 9.1 m.
The correct option is D.